A rotary viscosimeter which measures the viscosity characteristics of a sample liquid in an ultra-low fluid viscosity range by using the relaxation of a spiral spring is disclosed in a report entitled "A new method for the viscosity measurement of paint in setting, sagging, levelling and penetration shear rate range of 0.001 to 1.0 reciprocal seconds using a cone/plate spring relaxation technique", by T. C. Patton, Journal of paint technology, Vol. 38, No. 502, November 1966. This viscosimeter is a multi-purpose rotary viscosimeter having a cone/plate rotor in a measuring unit (Wells-Brookfield micro viscometer RTV cone plate model).
The summary of the structure of such a viscosimeter is shown in FIG. 4. The viscosimeter includes a scale disc 3 secured to a drive shaft 2 which is rotated by a driving motor 1 with a reduction gear. A rotor shaft 5 is connected with the lower end 21 of the drive shaft 2 via a spring 4. A sample liquid 9, the viscosity of which is to be measured, is disposed between a cone rotor 6 and a plate 7 below the lower end of the rotor shaft 5. This condition is enlarged and shown in FIG. 5.
On the other hand, a pointing needle 8 which extends above the scale disc is secured to the rotor shaft 5 so that the relative angular displacement between the drive shaft 2 and the rotor shaft 5 can be read from the position of the pointing needle 8 on the scale disc 3. If the torsional spring constant of the spring 4, the size of the rotor 6 and the rotational speed of the rotor are determined, the scale pointed to by the needle 8 on the scale disc 3 is proportional to the viscosity of the sample liquid. Accordingly, the viscosity can be determined from the scale pointed to by the needle 8.
In the description of the operation principle of the viscosimeter set forth in the above mentioned report, it is assumed that the rotor shaft 5, the rotor 6 and the pointing needle 8 are engaged with the lower end 21 of the drive shaft. However, the system of the rotor shaft 5 is unstable in such a structure. Accordingly, in an actual viscosimeter, the rotor shaft 5a is borne by a pivot 11 and a bearing 12 made of gemstone as shown in FIG. 6 so that the upper end of the rotor shaft 5a is prevented from swinging by a pin 13 penetrating into a hole in the shaft. The other parts are represented with reference numerals suffixed with a of the corresponding parts in FIG. 4. However, 4a corresponding to the spring 4 in FIG. 4 denotes a spiral spring. 17 denotes a jacket for maintaining the sample liquid at a constant temperature, to which circulating water is introduced from a separately provided constant temperature bath.
Since both the pointing needle 8a and the scale disc 3a are rotating during measurement of the viscosity in the present viscosimeter, it is hard to read the scale pointed to by the needle during the rotation of these parts. Accordingly, standard operation of the present viscosimeter is performed as follows: After the indicated point or the scale has become stable after starting the rotation of the viscosimeter, a clamp lever 14 of FIG. 6 is depressed downward with a finger to push up a push-up chip 15 around a fulcrum 14'. This causes a scale disc shaft 16 engaged with the push-up chip 15 and the scale disc 3a linked with the shaft 16 to be lifted upward. As a result of this, the pointing needle 8a is clamped relative to the scale disc 3a to keep the scale position while the pointing needle 8a is engaged with one of a number of knurled grooves (not shown) formed on the outer periphery of the scale disc 3a and is rotated together therewith.
The pointing needle 8a is stopped while clamped on the scale disc 3a when the motor is stopped in this state. Accordingly, the scale pointed to by the pointing needle can be easily read. When the clamp lever 14 is released, the pointing needle is disengaged from the scale disc 3a so that the pointing needle 8a is released to return to the "0" position on the scale disc.
The above-mentioned report teaches a viscosity measurement by a spring relaxation method using the relaxation of a spiral spring in the above mentioned viscosimeter. In the viscosity measurement using the spring relaxation technique, the rotor is manually rotated until the spiral spring of the viscosimeter assumes a full scale position (in which the pointing needle points to "100" on the scale). This operation is carried out without a measuring unit installed, and before the sample liquid is loaded between the coil and the plate so that the pointing needle is clamped in this position. Winding of the spiral spring is conducted by manually and slowly rotating the rotor at the lower end thereof until the pointing needle points to "100" on the scale. In order to fix the pointing needle in this position, i.e. to fix the spiral spring in the wound condition, the clamp lever is fixed in the depressed position, for example, by winding a rubber band around the lever after depressing the clamp lever. Thereafter, this condition is maintained until the lever is released for performing the actual viscosity measurement. Subsequently, the viscosity measurement is performed by the following steps.
A stopwatch is set to zero and the lever which fixes the pointing needle at "100" on the scale is released.
Simultaneously with this, the stopwatch is started. Then, the point on the scale which is indicated by the needle is read at appropriate intervals (for example, at intervals of 10 to 15 seconds at the start of the measurement cycle and at intervals of 30 seconds near the end). The measurement is completed over several minutes. The measurement is terminated when the change in reading since the previous reading becomes less than the minimum scale division.
Then, the thus obtained data are plotted on semilogarithmic graph paper. The readings are plotted on the logarithmic scale (two cycles) and the time data are plotted on linear scale.
The resultant curves are exemplarily illustrated in FIG. 7. The viscosity at a desired point on the curve, the shear stress corresponding to this point and the rate of shear are determined as follows:
The shear stress is determined from a coordinate value on the logarithmic axis, through which a horizontal straight line is drawn leftward from a point to be determined. The reading is proportional to the shear stress and can be converted into the shear stress represented in dyne/cm.sup.2 by multiplying it by an appropriate constant.
If the maximum torque (corresponding to the full scale 100) of the spiral spring of the viscosimeter is represented by M.sub.100, the torque Ms relative to the desired scale S is represented by a formula (1). EQU Ms=(S/100)M.sub.100 ( 1)
As shown in the enlarged view of the cone rotor portion of FIG. 5, the relation between the shear stress applied upon the sample liquid loaded between the rotating cone of the viscosimeter and the stationary plate and the torque M applied upon the cone is represented by a formula (2). EQU .tau.(shear stress)=3M/2.pi.r.sup.3 ( 2)
wherein r denotes the radius of the cone. A formula (3) is obtained by putting the formula (1) into the formula (2). EQU .tau.s=3(S/100)M.sub.100 /2.pi.r.sup.3 ( 3)
wherein .tau. s is the shear stress applied upon the sample liquid when the point on the scale is S.
A case in which the pointing needle is preliminarily clamped in the position of the scale S is firstly considered. Although
a torsional reaction force of the spiral spring is applied upon the rotor in this phase, the rotor is prevented from rotating by a clamp mechanism. When clamping of the rotor is released on starting the measurement (t=O), the spiral spring is relaxed so that the rotor commences rotating.
If the change in the indicated point on the scale during a very short period of time dt is represented as ds, a very small angle d.theta. (in radian) by which the pointing needle is moved during the period of time dt is represented by formula (4). EQU d.theta.=(ds/C)2.pi. (4)
wherein constant C denotes the full scale value which is obtained by dividing by 360 at the same graduation pitch at which the scale reads 100 on the scale plate of the viscosimeter.
If the rotational angular speed of the pointing needle at the desired time is represented as radian/second, .omega.=d.theta./dt. A formula (5) is obtained if d in the formula (4) is converted into this representation. EQU .omega.=d.theta./dt=(ds/dt)(2.pi./C) (5)
The shear rate D is represented by a formula (6) in consideration of the shape of the cone in the cone/plate viscosimeter. EQU D=.omega./.alpha. (6)
wherein .omega. and .alpha. denote the rotational angular velocity and the angle of the cone, respectively.
A formula (7) is obtained by putting .omega. in formula (5) into formula (6). EQU D=(ds/dt)(2.pi./C.alpha.) (7)
The viscosity .eta. of the sample liquid is defined as the ratio of the shear stress to the shear rate. In other words, the basic formula of the viscosity is given by a formula (8). EQU .eta.(viscosity)=.tau.(shear stress)/D(shear rate) (8)
A formula (9) is obtained by putting D in formula (7) and in .tau.s formula (3) into formula (8) and by rearranging it. EQU ds/S=(3M.sub.100 C.alpha./4.pi..sup.2 r.sup.3 100.eta.)dt (9)
From (9), EQU dlnS=(3M.sub.100 C.alpha./4.pi..sup.2 r.sup.3 100.eta.)dt EQU .eta.=(3M.sub.100 C.alpha./4.pi..sup.2 r.sup.3 100)/(dlnS/dt)(10)
Since the values in the parentheses are determined by the graduation dividing specification of the full scale torque scale plate of the spiral spring in the viscosimeter, the cone size, and the angle, they are determined by the design of the viscosimeter. Accordingly, the formula (9) can be simplified as represented by formula (11). EQU K=3M.sub.100 C.alpha./4.pi..sup.2 r.sup.3 100.2.3 EQU -.eta.=K/(d log S/dt) (11)
From the formula 11, the viscosity at a desired point on the curve which is obtained as shown in FIG. 7 is obtained by drawing a straight line which is tangential to that point. The viscosity .eta. can be determined by the calculation based upon the in proportional relation of the viscosity with the gradient d log S/dt as is given by the formula 11. The shear stress .tau.s and the shear rate D in this point can be determined by the relations set forth in formulae (3) and (8), respectively. The values which are determined from the dimensions of the viscosimeter and the measurement data in such a manner are set forth in FIG. 7.
The foregoing is the gist of the above-mentioned report. When the viscosity measurement using the spring relaxation technique is performed in the above mentioned conventional art, the clamp lever should be fixed by a rubber band in order to clamp the pointing needle by preliminarily manually rotating a rotor so that the spiral spring is wound to a full scale position and by depressing a needle clamp lever. When the measurement is started, it is necessary to remove the rubber band while the needle clamp lever is depressed with a finger and to read the pointed scale at predetermined intervals which are timed from the start of the measurement, when a finger is released from the clamp lever, while looking at a watch. There are problems that this operation is not only very troublesome, but also two operators are necessary to read the pointed scale and to record it while looking at a watch.